Mike Daum added 14 points, including 4 of 6 from 3-point range, for the Jackrabbits (10-2), who have won four of their last five games.
South Dakota State trailed 47-46 with 3:42 left, but Jake Bittle made a layup sparking a quick 5-0 run that gave the Jackrabbits a four point lead which they held to the end.
Christian Terrell scored a layup for the Eagles (6-5) to cut the South Dakota State lead to 51-49 with 1:25 to go. But the Jackrabbits made 5 of 6 at the free throw line over the final 40 second to close it out.
Marc Eddy Norelia scored 26 points and had 11 rebounds to lead Florida Gulf Coast.